Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

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0
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1answer
69 views

What is the name of this property of a set?

Let $S$ have property $P$ if there exists a function $f(x,y)$ such that: the domain of $f$ is $(S,S)$ the range of $f$ is $(-1,0,1)$ if $f(a,b) = 1$ and $f(b,c) = 1$ then $f(a,c) = 1$ and if $f(a,b) =...
1
vote
0answers
37 views

Is it an absorbing state if it does not communicate with other states?

$$\begin{matrix} 1 & 0 & 0\\ 0 & 0.5 & 0.5\\ 0 & 0.5 & 0.5 \end{matrix}$$ Given that this is a right transition matrix, would you call the state in the first row, say A, an ...
5
votes
3answers
129 views

Why there is no value for $x$ if $|x| = -1$? [duplicate]

According to the definition of absolute value negative values are forbidden. But what if I tried to solve a equation and the final result came like this: $|x|=-1$ One can say there is no value for $x$...
0
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0answers
32 views

What does Hilbert series of Monomial ideal describe?

I am trying to understand the point of hilbert series of monomial ideals. I am confused because Macaulay has commands for hilbertSeries, hilbertPolynomial and hilbertFunction. What does Hilbert ...
0
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0answers
25 views

Does this modulo-based function have a name?

Consider the scalar periodic function $$ f_{l,u}(x) = ((x - l) \mod (u - l)) + l $$ Where $l$ and $u$ are a lower and upper bound with $l < u$, so that the modulus $u - l$ is always positive and ...
1
vote
0answers
17 views

Terminology - idempotent and nilpotent maps

Recall that a map $f:X\to X$ is idempotent when $f(f(x)) = f(x)$. Is there a standard term for maps where, for some $n$ possibly bigger than $1$, for all $x$ one has $f( f^{n}(x)) = f^n(x)$? I am ...
1
vote
2answers
24 views

Terminology: matrix diagonalizable as a bilinear form

If a matrix $P$ is such $P^{-1}MP$ is diagonal, we say that $P$ diagonalizes $M$ (implicitly, as the matrix of an endomorphism). Now, if $P^\top M P$ is diagonal, is it correct to say that $P$ ...
0
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2answers
82 views

What is the set of all premises called?

An argument has two parts, the set of all premises, and the conclusion drawn from said premise. Now since there's only 1 conclusion, it would be weird to choose a name for the 'second' part of the ...
1
vote
0answers
20 views

Type of a total function where the first parameter is a partial function

Consider any partial function $f \colon \subseteq X \to Y$ for arbitrary sets $X,Y$. Now assume that a total function $g$ takes any such function $f$ as a first paramter and as a second parameter a ...
25
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3answers
4k views

What is this operator called?

If $x \cdot 2 = x + x$ and $x \cdot 3 = x + x + x$ and $x^2 = x \cdot x$ and $x^3 = x \cdot x \cdot x$ Is there an operator $\oplus$ such that: $x \oplus 2 = x^x$ and $x \oplus 3 = {x^{x^x}}$? ...
0
votes
1answer
53 views

Why do we say pi is the ratio of the circumference to the diameter, and not diameter to the circumference?

Everywhere I see it written, $\pi$ is described as "the ratio of the circumference to the diameter". I know $\pi = C/d$, but the ratio $3.14...:1$ is $3.14$... diameters to $1$ circumference. So ...
-4
votes
2answers
71 views

In “10 grams of salt”, is the unit “grams”?

The gram is a unit of mass, so "10 grams" has "grams" as the unit. "10 pounds" uses a different unit. So what is the "salt" in "10 grams of salt", if not a unit? In other words, what is the ...
0
votes
1answer
16 views

How should I refer to “volume-like” measures in a dimensional-free way?

When I try to model diffuse defined objects, I Frequently found myself in the need to refer to a measure in a way independent of the dimensional attributes of the space of definition of the objects. ...
1
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0answers
31 views

What are “boundaries” (as defined here) really called and where can I learn more?

My guess is that boundaries (perhaps under a different name) in graph theory are probably defined like this: Definition 0. Let $G$ denote a graph, $A$ denote a subset of $G$. Then a candidate ...
0
votes
1answer
35 views

How is immortality defined for a digraph?

A presentation on immortality $m$ of a digraph was presented almost as a sink $i\rightarrow m \leftarrow j$ somehow related on conditional independence and markov equivalence classes. I am confused ...
1
vote
1answer
40 views

entry vs. component

When speaking about tuples, I used to say and write "The number $a$ is the first component of the tuple $(a,b,c)$, and $c$ is its last component". This all went well until I had to speak about ...
0
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3answers
28 views

How to read this ArgMax definition in plain english

I was reading on Wikipedia about Argmax (https://en.wikipedia.org/wiki/Arg_max) and they gave the following equation. While I get most of this line, how would you read the following in plain English? ...
1
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0answers
44 views

Is there a special name for polynomials related by Möbius tranformation of the variable?

If we take a general polynomial with complex coefficients: $$C_n z^n+C_{n-1}z^{n-1}+\dots+C_1z+C_0$$ We can apply a general Möbius tranformation to the variable: $$z=\frac{aw+b}{cw+d},~~~~a,b,c,d \...
4
votes
1answer
40 views

What is the name for a function that behaves symmetrically when its arguments are scaled?

In other words, is there a name for this property of a function $f$: $$f(\alpha x_1,x_2,\ldots,x_n) = f(x_1,\alpha x_2,\ldots,x_n) = \ldots = f(x_1,x_2,\ldots,\alpha x_n)$$ Edit: I appreciate the ...
1
vote
2answers
38 views

What is the difference between exponential growth and decay?

A colleague came across this terminology question. What are the definitions of exponential growth and exponential decay? In particular: 1) Is $f(x)=-e^{x}$ exponential growth, decay, or neither? 2) ...
0
votes
1answer
36 views

What are pullbacks of finite-coproduct injections along arbitrary morphisms?

I am studying a definition of an extensive category: An extensive category is a category $E$ with finite coproducts such that pullbacks of finite-coproduct injections along arbitrary morphisms exist ...
3
votes
1answer
69 views

The maximal rotation matrix

Let's consider two numbers calculated for a rotation matrix which are: $s_e=$ the sum of all entries of a matrix $s_a=$ the sum of absolute values of all entries for a given matrix. It ...
0
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1answer
13 views

Etymologies of injections and surjecteions

Why one-to-one functions are called "injections" and onto functions are called "surjections"?
1
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1answer
45 views

Is there a generally accepted name for the described property of arrow $f$?

Let $F:\mathcal A\to\mathcal E$ denote a functor. Let $f:a\to b$ be an arrow in $\mathcal A$ that has the following property: For every arrow $g:a\to c$ in $\mathcal A$ and every arrow $h:Fb\to Fc$ ...
3
votes
4answers
78 views

Does this thing I'm calling 'the operationalization of $x$' have an accepted name?

Given a set $X$ and an element $x \in X$, we can turn $x$ into a function denoted $\tilde{x}$ as follows: for any set $Y$ and any function $f : X \rightarrow Y$, define $$\tilde{x}(f) = f(x).$$ For ...
3
votes
1answer
25 views

What is the term of a component drawn surrounded by another component?

Having a drawing (see image) of an undirected graph $G=(V,E)$ where $V = \{A,B,C,D,E,F,G\}$ and $v \in V$ $E = \{\{A,B\},\{B,C\},\{C,D\},\{D,A\},\{D,E\},\{E,F\},\{F,G\},\{G,E\}\}$ each vertex $v$ ...
2
votes
1answer
40 views

What do you call a directed graph in which reachablility is a symmetric relation?

Let $(N,E)$ a directed graph in which, if $a$ is reachable from $b$, then $b$ is also reachable from $a$. In other words, if $a$ and $b$ lie on a common path, then they also lie on a common cycle. ...
3
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2answers
101 views

Motivation behind word quotient

Why set of all cosets of a subspace W of a vector space V is called quotient space. What is the motivation behind word quotient?
3
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1answer
45 views

$\binom{n}{k}$ is a “binomial coefficient;” $n \; P \; k$ is a “__________.”

If I want to search for information concerning $\binom{n}{k}$, I can't Google that symbol directly, nor can I search for something like "n C k" and get anything relevant, but because the term "...
0
votes
2answers
179 views

What is the “taxonomy” or “hierarchy” (partial ordering) of algebraic objects used to attempt to capture geometric intuition? [closed]

What follows is a list of terms all of whose relationships to one another I have never fully succeeded in establishing, despite having spent much of 6-8 years trying to so. Feel no need to give ...
1
vote
2answers
43 views

What is the mathematical term describing a pipe or a tube?

I am interested in this unanswered question Pipe-fitting conditions in 3D and so I was trying to find information about it. If the 3D curve $f(x(t), y(t), z(t)) = 0$ is a line I think that the pipe ...
-4
votes
1answer
51 views

Piecewise Contextuous Functions - A possible new branch of functions?

Let us define f(x) as the following: $$f(x) = \begin{cases} g(x) & \text{if f(x) is being floored ($\lfloor x \rfloor$)} \\ h(x) & \text{if multiplication by anything other than 1 is being ...
3
votes
1answer
72 views

Is there a name for matrices that are symmetric along the cross diagonal? [duplicate]

Something like $$ A= \begin{bmatrix} a & b & c\\ b & d & e\\ c & e & f \end{bmatrix} $$ would be a symmetric matrix because the values are reflected along the ...
26
votes
7answers
3k views

Is there such a thing as a matrix of functions?

Do we ever put functions as entries of a matrix? If so, are these matrices used in linear algebra or do they have some other special use? There have been minor not neccessarily conflicts per se, but ...
2
votes
0answers
52 views

How does one read a formula with subscripts and superscripts?

An expression like $\Gamma_{ij}^k$ seems to be pronounced "gamma sub i, j upper k". Is this a generally accepted usage? Question. Is there a quotable source for such usage? Note that $k$ is not a ...
3
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0answers
46 views

How are varieties related polynomials?

My teacher says that varieties and ideals are related to each other while I tend to mix polynomials and varieties in my terminology. Could some explain how varieties are related to polynomials? And ...
0
votes
0answers
9 views

Terminology for operation on matrices to check psd

This is just a question of terminology. For defining positive definiteness or negative definiteness of a square $n\times n$ matrix $A$ (say if all entries of $A$ are real numbers) one asks whether $...
5
votes
1answer
51 views

Is it incorrect to call the probability mass function by the name “discrete probability density function”?

Commonly, the probability density function (pdf) is used when dealing with continuous random variables, while the probability mass function (pmf) is used for discrete random variables. This also ...
0
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0answers
16 views

Demonstration of Cycle-cut duality on elementary graphs?

I want to see examples on the Duality theorem between cycles and cuts on the page 26 of Graph Theory Electronic Edition 2005 by Reinhard Diestel. How to demonstrate the duality theorem between ...
2
votes
2answers
66 views

Why is matrix multiplication called 'multiplication' if it is non-commutative?

This question begins with the assumption that matrix multiplication was termed 'multiplication' as a form of comparison/parallel to multiplication of integers and real numbers. Why was matrix ...
104
votes
13answers
11k views

Why do we use the word “scalar” and not “number” in Linear Algebra?

During a year and half of studying Linear Algebra in academy, I have never questioned why we use the word "scalar" and not "number". When I started the course our professor said we would use "scalar" ...
0
votes
1answer
34 views

Portuguese term for “path metric”

Do anybody knows what is the usual translation to Portuguese for "path metric"? (Given a metric space $(M,d)$, $d$ is called a "path metric" if, given any pair $(x,y)\in M\times M$, there exists a ...
1
vote
1answer
22 views

Name for submodule killed by a right ideal

Let $\mathfrak a$ be a right ideal in a ring $R$. The set $N=\{m\in M: \mathfrak am=\mathfrak 0\}$ is a submodule of the left $R-$module $M$: If $m,n\in N$, $a\in \mathfrak a$, then $a(m-n) = am-an =...
3
votes
2answers
52 views

What is the name of the following bad “average”?

Is there a standard name for the "average" of the fractions $a/b$ and $c/d$ as $$ \frac{a+c}{b+d} \, \large ? $$ I understand that such an average is not unique in the sense that although $(2a)/(2b) = ...
2
votes
2answers
85 views

Why the word “projective” for $PGL_n(\mathbb{F})$?

I wrote the title for this question exactly as I had it exactly in my mind. Let me denote by $G=GL_n(\mathbb{F})$ for simplicity; I was working throughout the previous years many times with the ...
1
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0answers
18 views

Are there established names and/or symbols for these orderings?

Consider the following orderings on $\mathbb{Z}^2$. Say $(a, b) \leq_1 (c, d)$ if $a \leq c$ or if $a = c$ and $b \geq d$. So for instance $$(1,3) <_1 (1,2) <_1 (1,1) <_1 (2, 3) <_1 (2,...
7
votes
1answer
90 views

What does the word “norm” stands for in linear algebra?

I know that "norm" is the formal name for length, but where did this name came from? or from what language is came from? Thank you in advance.
2
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0answers
19 views

Is there a name for this acyclic quiver?

Sorry for the trivial question, but I don't know much about the subject and don't seem to be able to come up with much by Googling. Is there an established name for quivers of the form $$\require{...
0
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1answer
22 views

Characteristics and Mantessa

I've just heard about these terms. Could someone elaborate on what's their use is? And plus could you explain it using a few examples?
1
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2answers
61 views

Explain Example on Maximal Element with sets

I am trying to understand maximal element and I cannot understand this example from Wikipedia As an example, in the collection $$S = \{\{d, o\}, \{d, o, g\}, \{g, o, a, d\}, \{o, a, f\}\}$$ ...